Production of heavy quark flavors in proton-antiproton collisions with a center-of-mass energy of 1.8 $\times$ 10$\sp{12}$ electron volts is studied for events containing hadronic jets with a nearby muon track, where both the jet and the muon are produced at large angles from the incident beams. The muon tracking system and pattern recognition are described. Detailed calculations of the muon background due to meson decay and hadron noninteractive punchthrough are presented, and other background sources are evaluated. Distributions of muon transverse momentum relative to the beam and the jet axis agree with QCD expectations for semileptonic charm and beauty decay. Muon identification cuts and background subtraction leave 57.5 $\pm$ 17.1 muon-jet pairs, a rate consistent with the established production cross sections for charm and beauty quarks and the acceptance for minimum ionizing particles overlapping with nearby jets. A small dimuon sample clarifies the muon signature. No signatures of undiscovered phenomena are observed in this new energy domain.